Relaxation to equilibrium of conservative dynamics II: non-gradient exclusion processes

For the speed-change exclusion process on ${\mathbb{Z}}^d$ reversible with respect to the product Bernoulli measure, we prove that its semigroup $P_t$ satisfies a variance decay $\mathrm{Var}[P_{t}u]=C_u{t}^{-\frac{d}{2}}+o(t^{-\frac{d+\delta }{2}})$ for every local function $u$, with the constant $C_u$ explicitly characterized. This extends the result of Janvresse, Landim, Quastel and Yau in [Ann. Probab. 27(1) 325–360, 1999] to a non-gradient model. The proof combines the regularization argument in the previous work, and the chaos expansion in [Markov Process. Related Fields, 5(2) 125–162, 1999] by Bertini and Zegarlinski, via a new input from the homogenization theory.